The sample with largest number of atoms is

Options

A. 1g of `O_(2)(g)`
B. 1g of Ni (s)
C. 1g of B(s)
D. 1g of `N_(2)(g)`

Explanation

To determine which sample has the largest number of atoms, we will calculate the number of moles for each substance given in the options and then convert that to the number of atoms using Avogadro's number.

### Step-by-Step Solution:

1. **Identify the options and their molar masses:**
- **Oxygen (O2)**: Molar mass = 32 g/mol (since O has a molar mass of 16 g/mol and O2 has 2 oxygen atoms).
- **Nickel (Ni)**: Molar mass = 58.7 g/mol.
- **Boron (B)**: Molar mass = 11 g/mol.
- **Nitrogen (N2)**: Molar mass = 28 g/mol (since N has a molar mass of 14 g/mol and N2 has 2 nitrogen atoms).

2. **Calculate the number of moles for each sample:**
- For **1 gram of Oxygen**:
\[ \text{Moles of O2} = \frac{1 \text{ g}}{32 \text{ g/mol}} = 0.03125 \text{ moles} \]
Number of atoms = \(0.03125 \text{ moles} \times 2 \text{ (for O2)} \times N_A\)

- For **1 gram of Nickel**:
\[ \text{Moles of Ni} = \frac{1 \text{ g}}{58.7 \text{ g/mol}} \approx 0.0170 \text{ moles} \]
Number of atoms = \(0.0170 \text{ moles} \times N_A\)

- For **1 gram of Boron**:
\[ \text{Moles of B} = \frac{1 \text{ g}}{11 \text{ g/mol}} \approx 0.0909 \text{ moles} \]
Number of atoms = \(0.0909 \text{ moles} \times N_A\)

- For **1 gram of Nitrogen**:
\[ \text{Moles of N2} = \frac{1 \text{ g}}{28 \text{ g/mol}} \approx 0.0357 \text{ moles} \]
Number of atoms = \(0.0357 \text{ moles} \times 2 \text{ (for N2)} \times N_A\)

3. **Calculate the number of atoms for each sample:**
- **Oxygen**:
\[ \text{Atoms} = 0.03125 \times 2 \times N_A = 0.0625 N_A \]
- **Nickel**:
\[ \text{Atoms} = 0.0170 \times N_A = 0.0170 N_A \]
- **Boron**:
\[ \text{Atoms} = 0.0909 \times N_A = 0.0909 N_A \]
- **Nitrogen**:
\[ \text{Atoms} = 0.0357 \times 2 \times N_A = 0.0714 N_A \]

4. **Compare the number of atoms:**
- Oxygen: \(0.0625 N_A\)
- Nickel: \(0.0170 N_A\)
- Boron: \(0.0909 N_A\)
- Nitrogen: \(0.0714 N_A\)

5. **Conclusion:**
The sample with the largest number of atoms is **1 gram of Boron**, as it has the highest calculated number of atoms.

### Final Answer:
The sample with the largest number of atoms is **1 gram of Boron**.